Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-27225.2-f
Conductor 27225.2
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 3 \); class number \(1\).

Elliptic curves in class 27225.2-f over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.2-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
27225.2-f1 \( \bigl[a\) , \( a\) , \( 0\) , \( -3755 a - 17754\) , \( -313015 a - 857265\bigr] \)
27225.2-f2 \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 1738 a - 2624\) , \( 2648 a + 21893\bigr] \)
27225.2-f3 \( \bigl[a\) , \( a\) , \( 0\) , \( -3645 a - 18249\) , \( -321166 a - 799548\bigr] \)
27225.2-f4 \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 21648 a - 26219\) , \( 1749954 a - 331009\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph